The Floating Spherical Gaussian FSGO Model

In standard quantum-mechanical molecular structure calculations, we normally work with a set of nuclear-centred atomic orbitals Xi Xi CTOs are a good choice for the if only because of the ease of integral evaluation. Procedures such as HF-LCAO then express the molecular electronic wavefunction in terms of these basis functions and at first sight the resulting HF-LCAO orbitals are delocalized over regions of molecules. It is often thought desirable to have a simple ab initio method that can correlate with chemical concepts such as bonds, lone pairs and inner shells. A theorem due to Fock (1930) enables one to transform the HF-LCAOs into localized orbitals that often have the desired spatial properties. 

In the case of ammonia, which has ten electrons, we would choose five 1 s-type GTOs Xi, Xi Xs appropriate and write an electronic wavefunction 

A geometry optimization can be done if required, using any of the standard methods. 

There are a few interesting points about the treatment. First of all, there is no variational HF-LCAO calculation (because every available x is doubly occupied) and so the energy evaluation is straightforward. For a wavefunction comprising m doubly occupied orthonormal x s the normalizing factor N is 

In the case that the x s are individually normahzed but not necessarily orthogonal then the overlap integrals between the basis functions have to be taken into account. If we write the matrix of overlap integrals S and its determinant det S then 

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THE FLOATING SPHERICAL GAUSSIAN ORBITAL MODEL (FSGO)... 

The last approach dealt with in this section is the Floating Spherical Gaussian Orbital (FSGO) model and related methods. The original FSGO model introduced fay Frost is very simple. It treats chemical bonds in terms of localized orbitals, in a very close correspondence with chemical concepts. Each localized orbital (inner... 

Specifically, floating spherical Gaussian orbitals (FSGO), developed from an extension of Frost s simple electron pair model of molecular electronic structure, are used as basis functions in SCF-MO and Cl calculations. As will be described in the following section, these functions, unlike atomic basis orbitals, generally are not confined to atoms, but are allowed to occupy electron-rich regions corresponding... 

To investigate microscopic effects, the basis set used to obtain supermolecule descriptions and point charge models derived therefrom is a set of floating spherical Gaussian orbitals (FSGO), defined [4] as... 

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